How does God answer the supplication of a parent against their child, or the supplication of one overcome by sleep at night, despite His Almighty knowledge of what hearts conceal and that the supplication is not out of sincere conviction?

The prohibition against a parent supplicating against their child is firmly established and authentic. If Allah answers a parent's supplication against their child, it might be a punishment for the parent for violating the prophetic prohibition. Allah is not questioned about what He does, but they will be questioned. As for the hadith (definition) about drowsiness during prayer, it does not imply that a drowsy person might supplicate against themselves and Allah would answer it. Rather, the objective is to withdraw from prayer for fear of cursing oneself when intending to supplicate for oneself.